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Integrating maintenance and production decisions in a hierarchical production planning environment
Computers & Operations Research 26 (1999) 1059}1074
Integrating maintenance and production decisions in a hierarchical production planning environment夽 Larry Weinstein *, Chen-Hua Chung College of Business and Administration, Wright State University, Dayton, OH 45435, USA Decision Science and Information Systems Area, Gatton School of Management, The University of Kentucky, Lexington, KY 40506, USA
Abstract This article presents a three-part model to evaluate an organization's maintenance policy. In stage one, an aggregate production plan is generated using a linear programming formulation suggested by Chung and Krajewski (Operations Management 1984;4:389}406). In stage two, a master production schedule is developed to minimize the weighted deviations from the goals speci"ed by the aggregate production plan. In stage three, work center loading requirements, determined through rough cut capacity planning using resource pro"les, are used to simulate equipment failures during the aggregate production planning horizon. Several experiments are used to test the signi"cance of various factors for maintenance policy selection. These factors include the category of maintenance activity, maintenance activity frequency, failure signi"cance, maintenance activity cost, and aggregate production policy. Scope and purpose In order to resolve often con#icting objectives of system reliability and pro"t maximization, an organization should establish appropriate maintenance guidelines that take into consideration (1) costs associated with performing production activities, (2) costs associated with performing maintenance activities, and (3) the various costs associated with equipment failure and the resulting interruptions to the production plan. In currently prevailing practices, maintenance policy often is determined at the operational level in a political test between production and maintenance management. The resulting policy often is not optimal for the organization's overall objectives. 1999 Elsevier Science Ltd. All rights reserved.
* Corresponding author. Tel.: 937-643-1223; fax: 937-775-3545. 夽 This research was made possible through a grant from the Wright State University Strategic Initiatives Support Fund. 0305-0548/99/$ - see front matter 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 3 0 5 - 0 5 4 8 ( 9 9 ) 0 0 0 2 2 - 2
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1. Introduction Recent manufacturing trends have highlighted the need for increased consideration of the maintenance function. In these trends, we see an increased emphasis on the reduction of work-inprocess inventory, the improvement of equipment reliability, and improved productivity and quality [2]. This emphasis has prompted maintenance managers to operate in a proactive manner, coordinating their activities with production functions to ensure optimum productivity for the organization. This is particularly true for the capacity constrained organization, in which strict adherence to the production schedule is crucial. The production scheduling problem frequently is described as a disaggregation problem. The master production scheduling process disaggregates the aggregate production plan (APP) and translates it into speci"c timing and sizing requirements for production of individual end products, producing a feasible master production schedule (MPS) that meets the resource constraints of key work centers [3]. Krajewski and Ritzman [4] addressed the tasks relevant to the disaggregation problem in manufacturing and proposed a general disaggregation model for study of disaggregation production planning problems. Chung [5] and Chung and Krajewski [1] proposed a mixed integer linear programming model in which the APP was integrated with a model for master production scheduling. Recognizing the increased importance of the maintenance function, we now propose a model to link the maintenance planning function with aggregate production planning and master production scheduling activities. The Total Productive Maintenance (TPM) approach has suggested that maintenance planning indeed should be an integral part of the overall business strategy and should be coordinated and scheduled with manufacturing activities [6,7]. The successful implementation of such a program requires that maintenance activities be considered as integral parts of the production plan rather than as interruptions to that plan. Any violation of the maintenance schedule is treated as a violation of the production plan integrity, with the potential to jeopardize the stability of the production environment and the "nal assembly schedule (FAS). Traditional production plans often have failed to deal with the requirements of a proactive maintenance program because of production management's reluctance to accept the capacity constraints imposed by the service requirements of preventive maintenance activities. Historically, the relationship between production and maintenance has been con#ictual in nature. This attitude is perpetuated by the lack of communication regarding the scheduling requirements of each function [8]. Production management often views maintenance in the context of hours or days out of service and fails to realize the strategic importance of incorporating maintenance planning in the implementation of just-in-time (JIT) manufacturing. Management for the maintenance function, on the other hand, attempts to impose constraints on production that it deems necessary to achieve complete equipment reliability. Thus an issue that should be decided by the organization's strategic management often is settled at the operational level as a test of political clout. Failure to implement an optimum maintenance policy for the organization is the result. Determining an organization's most appropriate maintenance policy is far more complex than ascertaining the policy that minimizes equipment failure or maximizes equipment availability. In this article, we address the issues involved in the selection of the organization's optimum maintenance policy and present a model for the evaluation of maintenance policy to ensure global
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optimization. These issues are explored in the following set of four hypotheses, which are tested using the model described in this paper. The hypotheses are: Hypothesis 1. Integrating maintenance policy with aggregate production planning will signi"cantly in#uence total cost reduction. Hypothesis 2a. The e!ectiveness of integrating maintenance planning with production planning will escalate with increasing "nancial consequences for equipment failure. Hypothesis 2b. The e!ectiveness of integrating maintenance planning with production planning is signi"cantly reduced by increases in costs for performance of preventive and emergency maintenance activities. Hypothesis 3a. The frequency of preventive maintenance activities required for minimizing total costs is in#uenced by the "nancial consequences of equipment failure. Hypothesis 3b. The frequency of preventive maintenance activities required for minimizing total costs is in#uenced by the cost of performing preventive maintenance activities. Hypothesis 4a. In a production environment employing an aggregate strategy of level production, there will be a signi"cant di!erence in e!ectiveness for overall cost reduction between a policy of run-based preventive maintenance and interval-based preventive maintenance activities. Hypothesis 4b. In a production environment employing a chase aggregate strategy of varying production with demand, there will be a signi"cant di!erence in e!ectiveness for overall cost reduction between a policy of run-based preventive maintenance and interval-based preventive maintenance activities.
2. De5ning maintenance Maintenance is de"ned as the activities intended to preserve or promptly restore the safety, performance, reliability, and availability of plant structures, systems, and components to ensure superior performance of their intended function when required [9]. The maintenance function within an organization attempts to make capacity available to production in a reliable and stable manner to ensure responsive customer service, consistent product quality, reliable product output, cost e$cient operations, and high equipment utilization [10]. The optimum maintenance policy is de"ned as the maintenance policy that minimizes the sum of the total costs for performance of preventive and emergency maintenance activities; and the xnancial consequences of interruptions to the production plan for the organization [9]. The two primary categories of maintenance activities are emergency, or breakdown, maintenance and preventive maintenance. Emergency maintenance activities include repairs to production equipment when it exhibits signs of failure or after failure has occurred. Reliance solely on emergency maintenance is characterized as a reactive approach that may adversly a!ect both the integrity of the production plan and the quality of the product.
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Preventive maintenance is a proactive approach that supports the establishment of a JIT environment by studying situations that might interrupt the production plan. Its objective is to increase the reliability of a system over the long term by reducing wear, corrosion, fatigue, and related phenomena [11]. If plant management wants equipment to operate a larger percentage of time, the amount of preventive maintenance applied to that equipment should be increased [12]. As more resources are allocated to preventive maintenance activities, those required for emergency maintenance activities tend to decrease [8]. It should be noted, however, that scheduled maintenance will have a positive impact on reducing equipment failure only when the equipment exhibits an increasing failure rate [11,13]. The model described in this article provides for performance of both interval-based and run-based preventive maintenance activities. The interval-, or calendar-, based maintenance activities are divided into classes based on intervals of time. In this model, we use categories for weekly activities, monthly activities, and quarterly activities. We assume four weeks per month, 12 weeks per quarter, and 48 weeks per year. Run-based maintenance policies, which require preventive maintenance activities based on the cumulative usage of each work center, are set at levels ranging from every 25 h to every 4800 h of work center usage. It is assumed that the performance of any interval-based and run-based activity will return production equipment to `as-newa condition.
3. Phase one: The aggregate planning model Aggregate production planning is performed under managerial constraints that re#ect organization policy in regard to manpower adjustments, the holding of inventory, and outsourcing to other organizations. The APP attempts to minimize costs given a set of aggregate production and preventive maintenance requirements. The aggregate production planning model described in this article uses a mixed-integer linear programming (LP) formulation to determine the aggregate policies for the rate of production, inventory, regular and overtime workforce, and workforce smoothing activities. Subcontracting and backlogging are not considered at the aggregate level in this study. The model deals with the aggregate planning problem at the product family level. We de"ne a product family as a grouping of end items that share a common manufacturing setup. The model assumes that no scrap allowances and that no idle work in process inventories exist. This implies that the operations are at maximum e$ciency, where nothing is wasted or left idle. It assumes that all raw materials and components are available as required and that the workforce is completely interchangeable for di!erent operations at di!erent workstations. The aggregate model includes aggregate requirements for proactive maintenance activities speci"ed by the maintenance policy. Reactive maintenance activities are considered in the simulation
The following example is presented to clarify the di!erence between interval-based and run-based preventive maintenance policies: Changing the oil in your car every three months is an example of an interval-based maintenance policy. In contrast, changing the oil every 3000 miles, regardless of the time elapsed since the previous oil change, is an example of a run-based maintenance policy.
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model rather than at the aggregate level. Because we do not plan machine failure, the costs associated with these failures, including emergency maintenance, should not be included in the aggregate model. Because preventive maintenance activities are performed by machine operators in this model, the production and maintenance requirements share common labor and time resources at the aggregate level. LINGO software [14] is used to solve the aggregate model, with the program output exported to a "le for use in the second phase of the model, master production scheduling. The aggregate planning model is as follows: , 2 2 Min [s d(X )#v X #h I ]# [c H #c F #c O #c = ] GR GR GR GR GR GR FR R DR R MR R PR R G R R 2 ) # M d (M ) IR IR R I subject to , , 2 ) = #O ! a X ! b d(X )! k d (M )*0, I IR R R G GR G GR GR GR R I I !I #X "D , G R\ GR GR GR = != !H #F "0, R R\ R R O !h= )0, R R !Q d(X )#X )0, G GR GR d(X )"1 if X '0, GR GR if X "0, d(X )"0 GR GR X , I , H , F , O , = *0, GR GR R R R R where X production level (in units) of product family i in aggregate period t, GR I inventory level (in units) of product family i in aggregate period t, GR D demand (in units) for product family i in aggregate period t, GR H hiring (in labor hours) in aggregate period t, R F "ring (in labor hours) in aggregate period t, R O overtime (in labor hours) in aggregate period t, R = regular time workforce level (in labor hours) in aggregate period t, R v unit (variable) production cost of product family i in aggregate period t, GR h unit inventory carrying cost of product family i in aggregate period t, GR c hiring cost per labor hour, FR c "ring cost per labor hour, DR c overtime cost per labor hour, MR c regular time workforce cost per labor hour, PR
(1) (2) (3) (4) (5) (6)
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a average labor hours consumed by per unit output of product family i, G h fraction de"ning maximum allowed overtime in any period, N total number of product families, ¹ length of the planning horizon, k work center where maintenance activity is to be performed, s setup cost of product family i, GR d(X ) binary setup variable for product i in aggregate period t, GR b setup time in labor hours for product family i, G M cost per maintenance activity for work center k in period t, IR d (M ) maintenance variable for work center k in week t, IR k maintenance time in labor hours for work center k, I Q a large number used to ensure the e!ects of binary variables. G The "rst constraint ensures that the regular and overtime labor capacity for each aggregate period is su$cient for production, setup, and preventive maintenance activities. The maintenance binary variable for preventive maintenance activities is driven by the maintenance policy determined by the decision maker. For example, an interval-based seasonal maintenance policy implies that resources must be allocated for a single maintenance activity every three periods. Run-based policies, on the other hand, are translated into aggregate requirements based upon work center run times generated in the simulation using the product resource pro"les (Fig. 1) and the FAS. The speci"c length of time for each maintenance activity, k , is set by the requirements for the particular I work center. Constraint two is the basic inventory identity relationship for each product family. Constraint three expresses the workforce balance relationship from period to period. Constraint four states that the overtime used should not exceed a speci"ed percentage of the regular time workforce level in each period. Constraint "ve works as a surrogate constraint for the binary variables in constraint six. Constraint six forces d(X ) to zero when X '0. Q is de"ned as the GR GR G maximum production quantity for a product family during each aggregate period.
4. Phase two: The master schedule Master production scheduling is concerned with what is known as the lot sizing problem. In our model, the MPS is formulated using a multiple goal linear programming model. The MPS is solved using LINGO software [14] with data imported from the aggregate model. 2 , Min bIBI # (w\d\#w>d>) G GRY R R R G IZ)G RYZLR , 2 # (w\d\#w>d>#w\d\#w>d>) G GR G GR G GR G GR G R
In order to create an initial APP using run-based preventive maintenance activities, a "nal assembly schedule "rst must be generated based upon an APP without maintenance resource allocations. This procedure is described on Section 5.
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subject to II !II #XI #BI !BI "DI , RY\ GRY GRY GRY RY\ GRY G ( , (rI X )#d\!d> GKH G RY>G\K RY RY G IZIG K H , 2 ) "0.25 = ! b d(X )! k d (M ) , I IR R G GR G R I d>#d\!d>"0 , RY R R R RYZLR
(1 )
XI #d\!d>"X , GRY GR GR GR IZIG RYZLR
(4 )
(2 ) (3 )
(5 ) II #d\!d>"I , GRY GR GR GR IZIG RYZLR XI , II , BI , d\, d>, d\, d>, d\, d>, d\, d>*0, GRY GRY GRY GRY GRY GRY GRY GRY GRY R R where bI backorder cost per unit for end item k in family i, G wL weights assigned to deviation variables, G XI production quantity (in units) of end product k of product family i in period t , GRY II inventory (in units) of end item k of product family i in period t , GRY BI backorder (in units) of end item k of product family i in period t , GRY DI demand (in units) of end item k of product family i in period t , GRY d\ undertime in period t ; i.e., negative deviation from planned workforce level, RY d> overtime in period t ; i.e., positive deviation from planned workforce level, RY d\ negative deviation from planned aggregate production level of product family i in period t, GR d> positive deviation from planned aggregate production level of product family i in period t, GR d\ negative deviation from planned aggregate inventory level of product family i in period t, GR d> positive deviation from planned aggregate inventory level of product family i in period t, GR d\ negative deviation from planned overtime level, R d> positive deviation from planned overtime level, R rI number of labor hours required for processing item k of product family i at work center GKH j in the mth period since production started on k, assuming at most one operation for each item at each work center j. The objective function in this model attempts to minimize the sum of backordering costs and weighted deviations from goals for production, inventory, and overtime as established by the aggregate production planning model. The aggregate decisions from the previous phase appear as right-hand side values for a series of multiple goal constraints in the linear programming model. The model allows the user to set weights to re#ect the relative importance of each goal established in the aggregate production planning process. For this experiment all weights are set equal to one.
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Fig. 1. Product Resource Pro"les.
The "rst constraint is the inventory identity relationship with backorders incorporated for each item of a particular product family. The second constraint ensures that the total labor hours required at all work centers with undertime and overtime adjustments will not exceed the labor hour capacity planned, or available for, each disaggregate period. Information on the right-hand side obtained from the APP indicates the total labor hours planned for the aggregate period minus labor hours consumed for setups of all product families and for performance of preventive maintenance activities. The `0.25a converts the monthly aggregate "gures into weekly disaggregate
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quantities. The third constraint states that the use of overtime should be targeted at the overtime speci"ed in the aggregate plan. The fourth constraint states that the sum of all end item production quantities for the disaggregate periods (t ) shall be targeted at the aggregate family production levels established for the aggregate periods (t). The last constraint relates the sum of all item inventory quantities in each disaggregate period t to the inventory goal for each aggregate family established for that period t.
5. Phase three: Simulation of the master production schedule and maintenance plan In the third phase of the model, a discrete event simulation is used to evaluate the consequences of the work center loading required to satisfy the MPS established in the previous phase. The MPS, determined by the goal programming model, is exported into the simulation database. That database also contains the following information: the resource pro"les for all end items (Fig. 1), the values of the shape and scale parameters for the failure distribution of each work center, the values of the parameters for the distribution of the repair times for each work center, the hourly costs assigned to equipment emergency service time, and the activity times at which preventive maintenance activities occur. (Preventive maintenance costs are determined at the aggregate level and are not accrued in the simulation.) The model generates a report based on the results of 48 weeks of simulation activities. The report includes speci"c times of work center failure as determined by the simulation program; the lengths of the individual and total emergency repair times, also determined by the simulation program and based on service time distribution parameters; total work center run time; and failure cost for the speci"c maintenance policy, calculated using the treatment's hourly cost for emergency repair and the expected total repair time. The failure cost is added to the aggregate costs determined in the APP model to derive a total policy cost. The simulation program allows the user to evaluate the consequences of the maintenance policy on completion of the MPS. In order to evaluate an interval-based maintenance policy, the decision maker begins with the aggregate model and assigns to the appropriate aggregate periods the resource requirements for that policy. Next, the APP and an MPS are calculated. The simulation program evaluates the MPS and determines speci"c equipment failure times at each work center, the corresponding repair times for emergency maintenance, and total cost for the maintenance policy. In the case of a run-based maintenance policy, the entire model "rst must be run without maintenance resource requirements in order to determine the cumulative run times (CRTs) at each work center. These CRTs are used to assign resource requirements for run-based preventive maintenance activities in the aggregate model. The model then is rerun to generate the new CRTs and to determine the revised maintenance assignments. The process is repeated until the assignments for the run-based preventive maintenance activities for two consecutive runs are identical. The simulation results for the last set of maintenance assignments are used to evaluate that policy. Because the work center mean-time-to-failure values and the repair times generated by the simulation both are based on probability distributions, a degree of uncertainty obviously will be associated with the outcomes from the model. Therefore, each simulation has been replicated 50
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times, and the average value for the simulation results of each treatment has been used for the evaluation of the maintenance policy.
6. Experimental parameters In testing the four sets of hypotheses relating to integration of maintenance and production planning, 252 di!erent experimental treatments were used to model various combinations of policies for (1) maintenance policy, (2) the cost for performing each maintenance activity, (3) the cost used to re#ect the signi"cance of equipment failure, (4) a scale parameter to re#ect equipment failure, and (5) the aggregate strategy. For example, a treatment could call for a maintenance policy of quarterly activities, a maintenance activity cost of $20 per hour, a failure cost of $10 per hour, a scale parameter of 400 h, and a level aggregate strategy. The treatments are summarized in [9]. Experimental treatments for interval-based maintenance policies specify weekly activities, monthly activities, and quarterly activities. Experimental treatments for run-based maintenance policies specify 25, 100, or 400% of the equipment failure distribution scale parameter (in hours) of the Weibull distribution used to model the failure distribution of the work center. For example, when the scale parameter was set at 100 h, run-based policies for experimental treatments speci"ed preventive maintenance activities every 25, 100, or 400 h. The individual activity costs and times for preventive maintenance activities were set at three levels: $20 and one hour per activity, $40 and two hours per activity, and $100 and "ve hours per activity. This article will not investigate the issue of "nancial consequences of equipment failure to the organization. However, several possible consequences could result when equipment fails. For example, severely damaged equipment may require signi"cant expenditures for repair or replacement of parts. Equipment failure may also result in lost production time, with overtime cost penalties incurred when labor resources are used to perform corrective repairs rather than to satisfy production requirements. Unsatisfactory product quality may also result from equipment failure. Equipment experiencing failure may continue to produce parts that do not meet quality standards. These products will have to be inspected, evaluated, and then reworked or scrapped. A high failure cost environment suggests that stability for the production plan is important and that considerable "nancial consequences may result if that plan is interrupted. It may also indicate a premium cost penalty for emergency maintenance activities. A low failure cost environment implies that stability of the production plan is not critical and that the costs incurred from that instability are minimal. In our model, "nancial consequences are modeled by the cost per hour for unscheduled service time. Service times are randomly generated by the simulation model and follow a negative exponential distribution with a mean of "ve hours. The costs for unscheduled service times are set at $10, $50, and $100 per hour. For this experiment, these costs are assumed to be linear with respect to time. Lewis [11] suggests using the two-parameter Weibull distribution to model the distribution of equipment mean-time-to-failure. The shape parameter for the Weibull distribution was "xed at 2.0 for all treatments. This parameter determines the basic shape of the graph of the probability density function. The use of a positive value for the shape parameter indicates the equipment exhibits an increasing rate of failure and thus, would bene"t from the performance of preventive maintenance activities. The scale parameter represents the characteristic life of the distribution and was set at 100, 400, or 1200 h.
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Fig. 2. Summary of Cost Data for the Aggregate Production Planning Model.
The experiment simulated production at two work centers that process items speci"ed in the MPS. Machine loading was determined by rough cut capacity planning through resource pro"les technique using the production requirements speci"ed in Fig. 1. In this "gure, the product resource pro"les for four end items are illustrated. Each line indicates the work center in which the activity is performed, the week in which the activity is performed, and the length of time the activity requires. The production costs included in the APP model include the machine setups; the variable, or material cost for each product produced; costs for holding inventory; costs for hiring and "ring; costs for overtime; and costs for production labor. The production costs are summarized in Fig. 2.
7. The hypotheses Each of the research hypotheses used to test the four sets of hypotheses is repeated below, along with a brief description of the statistical test used. The test result is then summarized and conclusions stated. Hypothesis 1. Integrating maintenance policy with aggregate production planning will signi"cantly in#uence total cost reduction. Statistical analysis was performed at the Wright State University Statistical Consulting Center by Dr. Kathleen Beal.
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Research [15] has shown that managerial policies for aggregate production planning will have a signi"cant in#uence on the cost of the APP. The "rst hypothesis tests whether managerial policies for maintenance planning will have a similar in#uence by testing the e!ectiveness of using the model to reduce total costs for production, preventive maintenance, and emergency maintenance activities. The evaluation criterion for this hypothesis is percent reduction in total costs of a policy using preventive maintenance activities when compared to one relying solely on emergency maintenance activities. A two-tailed, one-sample t test is used to test this hypothesis at the 0.05 level of signi"cance. The calculated test statistic, t"2.6378, and the null hypothesis is rejected (0.01(p(0.02). The alternative, or research, hypothesis is accepted with the conclusion that integrating maintenance policy with aggregate production planning using our model will have a signi"cant in#uence on total cost reduction. Hypothesis 2a. The e!ectiveness of integrating maintenance planning with production planning will escalate with increasing "nancial consequences for equipment failure. Research has shown that the maintenance policy will a!ect the frequency of equipment failure [8]. Therefore, it is logical that the "nancial consequences of equipment failure will be an important factor in the e!ectiveness of this model in reducing costs. As costs associated with equipment failure increase, we would intuitively expect model e!ectiveness likewise to increase. The second hypothesis was tested using the Jonckheere distribution-free test for ordered alternatives. The null hypothesis states that the average e!ectiveness will not be a!ected by increasing "nancial consequence for equipment failure. This indicates that model e!ectiveness and "nancial consequences for equipment failure are independent. The alternative hypothesis states that the average e!ectiveness will increase with increasing "nancial consequences for equipment failure, indicating a relationship between model e!ectiveness and equipment failure. The resulting z score using the large sample approximation formulation is 7.968. Therefore the null hypothesis is rejected at a(0.00003. This clearly indicates that the e!ectiveness of integrating maintenance and production planning increases with escalating "nancial consequences for equipment failure. We can expect that our model will be more e!ective in an environment in which interruptions to the production plan are more signi"cant. Hypothesis 2b. The e!ectiveness of integrating maintenance planning with production planning is signi"cantly reduced by increases in costs for performance of preventive and emergency maintenance activities. This hypothesis tests whether the model e!ectiveness is in#uenced by increasing costs for performance of preventive and emergency maintenance activities. The Jonckheere distribution-free test for ordered alternatives is used to test this research hypothesis at two levels of maintenance costs. The test statistics are Z"4.032 (p(0.00003) and Z"3.438 (p"0.00029). The null hypothesis is rejected, indicating that the e!ectiveness of integrating maintenance planning with production planning signi"cantly decreases as costs for performing preventive and emergency maintenance activities increase relative to costs for production activities. This implies that as maintenance
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costs rise in relation to production costs and costs associated with equipment failure, the potential savings from integrating production and maintenance planning are reduced. Hypothesis 3a. The frequency of preventive maintenance activities required for minimizing total costs is in#uenced by the "nancial consequences of equipment failure. This research hypothesis proposes that there is a relationship between (1) frequency of preventive maintenance activities required by a particular maintenance policy necessary to minimize total costs and (2) "nancial consequences for equipment failure. This is to say that frequency of preventive maintenance activities in an optimum maintenance policy and failure signi"cance are dependent. As the "nancial consequences for equipment failure increase, one would expect total costs to be reduced when policies are adopted requiring increased frequency of preventive maintenance activities. The Chi-square test for independence was used to test this hypothesis. The test statistic of 31.0 indicates that the null hypothesis can be rejected at the a(0.005 level of signi"cance: There is a signi"cant interaction between the signi"cance of equipment failure and the frequency of preventive maintenance required to minimize total costs. Hypothesis 3b. The frequency of preventive maintenance activities required for minimizing total costs is in#uenced by the cost of performing preventive maintenance activities. This hypothesis examines whether there is a relationship (dependence) between frequency of preventive maintenance activities required in an optimal maintenance policy and the hourly cost of performing preventive maintenance activities. As the costs for performing individual preventive maintenance activities increases, one could intuitively expect that total costs for maintenance and production activities would be minimized by policies requiring performance of fewer preventive maintenance activities. The Chi-square test for proportions was used to test this research hypothesis at three levels of failure costs. The null hypothesis was rejected at the 0.005 level of signi"cance for two lower failure costs, but was only rejected at the 0.01 level of signi"cance for the highest level of failure costs. Chi-square values for the three test statistics moved from 31 to 22 to 14 as failure costs increased. This demonstrates that the frequency of preventive maintenance activities required in an optimum maintenance policy is signi"cantly in#uenced by the hourly cost of performing preventive maintenance activities. However, this in#uence appears to diminish as the signi"cance of equipment failure increases. Therefore, in selecting an optimal maintenance policy, the decision maker must consider the in#uences of both the hourly cost for performing preventive maintenance activities and the level of "nancial signi"cance for equipment failure. If either were to vary, the decision maker would need to reconsider the organization's maintenance policy. Hypothesis 4a. In a production environment employing an aggregate strategy of level production, there will be a signi"cant di!erence in e!ectiveness for overall cost reduction between a policy of run-based preventive maintenance and interval-based preventive maintenance activities.
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Hypothesis 4b. In a production environment employing a chase aggregate strategy of varying production with demand, there will be a signi"cant di!erence in e!ectiveness for overall cost reduction between a policy of run-based preventive maintenance and interval-based preventive maintenance activities. These hypotheses were used to test whether the aggregate strategy used in production planning has a signi"cant in#uence on the choice between a run-based or interval-based maintenance policy. A level aggregate production strategy prescribes a constant production rate. Once an appropriate interval for maintenance activities that would minimize total costs is selected, that policy remains optimum unless end item demand varies between aggregate periods. A chase aggregate production strategy, on the other hand, dictates that we vary production with changes in demand. If demand is constant, then production will be constant. If demand exhibits characteristics of seasonality or cycles, or if it simply varies randomly or according to some probability distribution, the volume of production activities would vary during the aggregate period. The activities called for by the maintenance policy might be optimum during one period, but inadequate to maintain the equipment during another. The Chi-square test for independence was used to test hypotheses 4a and 4b. For hypothesis 4a, the test statistic s"0.07407. The null hypothesis cannot be rejected at the a"0.05 level of signi"cance (0.75'p'0.90). This implies that in a production environment employing a level aggregate strategy, there will not be a signi"cant di!erence in overall cost reduction between using a policy of run-based preventive maintenance or of interval-based preventive maintenance activities. For hypothesis 4b, the test statistic s"16.16. The null hypothesis is rejected at the a"0.05 level of signi"cance (p(0.005). In a production environment employing a chase aggregate strategy, we can expect that run-based maintenance policies will be more e!ective than interval-based policies during a signi"cant portion of the time. The experiment results demonstrate that when there is a level aggregate strategy, there will not be a signi"cant di!erence in total cost when we select either a run-based or an interval-based policy. The hours of production at each work center will be constant during the aggregate planning period. In practice, therefore, an interval-based maintenance policy may be as equally e!ective as a runbased policy. In an environment employing a chase aggregate strategy, on the other hand, run-based maintenance policies generally will be more e!ective than interval-based policies and should therefore be selected by the decision maker.
8. Managerial implications In this study, we introduced a model that links selection of the organization's maintenance policy with the aggregate production planning process. We developed an experimental design and used it to evaluate a set of four hypotheses in order to test our model. The managerial implications of the test results are summarized below and may be used to guide decision makers in the application of this model. It should be noted, however, that the test results are subject to the assumptions of our experiment and cannot blindly be applied beyond the limitations of the experiment.
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E Under certain conditions, integrating maintenance and production planning is an e!ective approach to reducing total costs for production activities, preventive maintenance activities, and the costs associated with equipment failure. An integrated approach allows the decision maker to more accurately determine the point at which the sum of these is minimized. E The e!ectiveness of integrating maintenance planning with production planning in reducing total costs will increase as "nancial consequences for equipment failure increases. E The expense of performing preventive maintenance may be a signi"cant factor in determining the optimum maintenance policy. As the costs to perform preventive maintenance activities increase, the potential bene"t of integrating production and maintenance planning appears to decrease. That bene"t, however, is tied to the "nancial signi"cance of equipment failure. Neither factor should be considered without regard for the other. E As the "nancial signi"cance of equipment failure increases, organizations will minimize total costs by adopting maintenance policies requiring more frequent maintenance activities. E The frequency of maintenance activities required for an optimum maintenance policy is a!ected by the cost to perform preventive maintenance activities. As failure costs increase, and other factors remain unchanged, policies calling for more frequent maintenance activities will be optimal. This trend is blocked, however, when the production activity costs also increase. E The selection of an optimum maintenance policy is in#uenced by both aggregate production policy and end item demand pattern. An organization using a chase aggregate production strategy with a varying demand pattern should select a preventive maintenance policy based on equipment run time. An organization with a constant demand pattern will not signi"cantly bene"t from using one type of preventive maintenance policy over the other. E An organization using a level aggregate production strategy, under either a constant or varying demand pattern, also will not signi"cantly bene"t from using one type of maintenance policy over the other. Additional research from this study may follow several directions. One path might be to make an empirical study of manufacturing organizations, comparing the e!ectiveness of their current maintenance policies with the theoretical policy resulting from this model. Another direction might be to evaluate the impact of the model on schedule e!ectiveness measures such as throughout and makespan. A third direction would be to evaluate the in#uences of additional equipment failure and service distributions on the model's e!ectiveness. Each of these would be a natural extension of the research already conducted.
References [1] Chung CH, Krajewski LJ. Planning horizons for master production scheduling. Operations Management 1984;4:389}406. [2] Gilbert JP, Finch BJ. Maintenance management: keeping up with production's changing trends and technology. Journal of Operations Management 1985;6:1}12. [3] Vollmann TE, Berry WL, Whybark D. Manufacturing planning and control systems. Boston: Irwin, 1997. [4] Krajewski LJ, Ritzman LP. Disaggregation in manufacturing and service organizations. Decision Sciences 1977;8:1}18.
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[5] Chung CH. Planning horizons for aggregate planning and master production scheduling. Dissertation, Ohio State University, 1982. [6] Nakajima S. Introduction to TPM. Cambridge: Productivity Press, 1988. [7] Rhyne DM. Total plant performance advantages through total production maintenance. APICS Conference Proceedings, rpt. APICS Curricula and Certi"cation Council, 1991. [8] Rishel TD. A model of the e!ect of scheduled maintenance on manufacturing system capacity. Dissertation, The Pennsylvania State University, 1991. [9] Weinstein L. Decision support for the integration of maintenance activities with fron end production planning activities. Dissertation, The University of Kentucky, 1996. [10] Ettkin LP, Jahnig DG. Adapting MRP II for maintenance resource management can provide a strategic advantage. Industrial Engineering 1986;50}9. [11] Lewis EE. Introduction to reliability engineering. New York: Wiley, 1987. [12] Mann L. Maintenance management. Lexington, MA: D.C. Heath and Company, 1976. [13] Rishel TD, Cristy DP. Incorporating maintenance activities into production planning: integration at the master schedule versus material requirements level. unpublished manuscript. [14] LINGO. Lindo Systems Inc. Chicago, IL, 1992. [15] Mangiameli PM. The e!ects of managerial policies on aggregate plans, the master production schedule, and departmental plans. Dissertation, Ohio State University, 1979.
Larry Weinstein is an Assistant Professor of Operations Management at Wright State University in Dayton, OH 45435. He received his doctorate from the University of Kentucky in 1996. He has taught at Eastern Kentucky University and Ball State University. Dr. Weinstein teaches courses in Statistics, Operations Management, and Quality Management. Chen H. Chung graduated from Ohio State University with a Ph.D. in Production and Operations Management. He is currently Professor of Decision Science and Information Systems and Gatton Research Professor at School of Management, Gatton College of Business and Economics of University of Kentucky. He is Certi"ed Fellow in Production and Inventory Management (CFPIM) by APICS. Dr. Chung has published over forty articles in journals such as Journal of Operations Management, Decision Sciences, International Journal of Production Research, Production and Operations Management, European Journal of Operational Research, Computers & Operations Research, and the Journal of Manufacturing Management.
Integrating maintenance and production decisions in a hierarchical production planning environment夽 Larry Weinstein *, Chen-Hua Chung College of Business and Administration, Wright State University, Dayton, OH 45435, USA Decision Science and Information Systems Area, Gatton School of Management, The University of Kentucky, Lexington, KY 40506, USA
Abstract This article presents a three-part model to evaluate an organization's maintenance policy. In stage one, an aggregate production plan is generated using a linear programming formulation suggested by Chung and Krajewski (Operations Management 1984;4:389}406). In stage two, a master production schedule is developed to minimize the weighted deviations from the goals speci"ed by the aggregate production plan. In stage three, work center loading requirements, determined through rough cut capacity planning using resource pro"les, are used to simulate equipment failures during the aggregate production planning horizon. Several experiments are used to test the signi"cance of various factors for maintenance policy selection. These factors include the category of maintenance activity, maintenance activity frequency, failure signi"cance, maintenance activity cost, and aggregate production policy. Scope and purpose In order to resolve often con#icting objectives of system reliability and pro"t maximization, an organization should establish appropriate maintenance guidelines that take into consideration (1) costs associated with performing production activities, (2) costs associated with performing maintenance activities, and (3) the various costs associated with equipment failure and the resulting interruptions to the production plan. In currently prevailing practices, maintenance policy often is determined at the operational level in a political test between production and maintenance management. The resulting policy often is not optimal for the organization's overall objectives. 1999 Elsevier Science Ltd. All rights reserved.
* Corresponding author. Tel.: 937-643-1223; fax: 937-775-3545. 夽 This research was made possible through a grant from the Wright State University Strategic Initiatives Support Fund. 0305-0548/99/$ - see front matter 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 3 0 5 - 0 5 4 8 ( 9 9 ) 0 0 0 2 2 - 2
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1. Introduction Recent manufacturing trends have highlighted the need for increased consideration of the maintenance function. In these trends, we see an increased emphasis on the reduction of work-inprocess inventory, the improvement of equipment reliability, and improved productivity and quality [2]. This emphasis has prompted maintenance managers to operate in a proactive manner, coordinating their activities with production functions to ensure optimum productivity for the organization. This is particularly true for the capacity constrained organization, in which strict adherence to the production schedule is crucial. The production scheduling problem frequently is described as a disaggregation problem. The master production scheduling process disaggregates the aggregate production plan (APP) and translates it into speci"c timing and sizing requirements for production of individual end products, producing a feasible master production schedule (MPS) that meets the resource constraints of key work centers [3]. Krajewski and Ritzman [4] addressed the tasks relevant to the disaggregation problem in manufacturing and proposed a general disaggregation model for study of disaggregation production planning problems. Chung [5] and Chung and Krajewski [1] proposed a mixed integer linear programming model in which the APP was integrated with a model for master production scheduling. Recognizing the increased importance of the maintenance function, we now propose a model to link the maintenance planning function with aggregate production planning and master production scheduling activities. The Total Productive Maintenance (TPM) approach has suggested that maintenance planning indeed should be an integral part of the overall business strategy and should be coordinated and scheduled with manufacturing activities [6,7]. The successful implementation of such a program requires that maintenance activities be considered as integral parts of the production plan rather than as interruptions to that plan. Any violation of the maintenance schedule is treated as a violation of the production plan integrity, with the potential to jeopardize the stability of the production environment and the "nal assembly schedule (FAS). Traditional production plans often have failed to deal with the requirements of a proactive maintenance program because of production management's reluctance to accept the capacity constraints imposed by the service requirements of preventive maintenance activities. Historically, the relationship between production and maintenance has been con#ictual in nature. This attitude is perpetuated by the lack of communication regarding the scheduling requirements of each function [8]. Production management often views maintenance in the context of hours or days out of service and fails to realize the strategic importance of incorporating maintenance planning in the implementation of just-in-time (JIT) manufacturing. Management for the maintenance function, on the other hand, attempts to impose constraints on production that it deems necessary to achieve complete equipment reliability. Thus an issue that should be decided by the organization's strategic management often is settled at the operational level as a test of political clout. Failure to implement an optimum maintenance policy for the organization is the result. Determining an organization's most appropriate maintenance policy is far more complex than ascertaining the policy that minimizes equipment failure or maximizes equipment availability. In this article, we address the issues involved in the selection of the organization's optimum maintenance policy and present a model for the evaluation of maintenance policy to ensure global
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optimization. These issues are explored in the following set of four hypotheses, which are tested using the model described in this paper. The hypotheses are: Hypothesis 1. Integrating maintenance policy with aggregate production planning will signi"cantly in#uence total cost reduction. Hypothesis 2a. The e!ectiveness of integrating maintenance planning with production planning will escalate with increasing "nancial consequences for equipment failure. Hypothesis 2b. The e!ectiveness of integrating maintenance planning with production planning is signi"cantly reduced by increases in costs for performance of preventive and emergency maintenance activities. Hypothesis 3a. The frequency of preventive maintenance activities required for minimizing total costs is in#uenced by the "nancial consequences of equipment failure. Hypothesis 3b. The frequency of preventive maintenance activities required for minimizing total costs is in#uenced by the cost of performing preventive maintenance activities. Hypothesis 4a. In a production environment employing an aggregate strategy of level production, there will be a signi"cant di!erence in e!ectiveness for overall cost reduction between a policy of run-based preventive maintenance and interval-based preventive maintenance activities. Hypothesis 4b. In a production environment employing a chase aggregate strategy of varying production with demand, there will be a signi"cant di!erence in e!ectiveness for overall cost reduction between a policy of run-based preventive maintenance and interval-based preventive maintenance activities.
2. De5ning maintenance Maintenance is de"ned as the activities intended to preserve or promptly restore the safety, performance, reliability, and availability of plant structures, systems, and components to ensure superior performance of their intended function when required [9]. The maintenance function within an organization attempts to make capacity available to production in a reliable and stable manner to ensure responsive customer service, consistent product quality, reliable product output, cost e$cient operations, and high equipment utilization [10]. The optimum maintenance policy is de"ned as the maintenance policy that minimizes the sum of the total costs for performance of preventive and emergency maintenance activities; and the xnancial consequences of interruptions to the production plan for the organization [9]. The two primary categories of maintenance activities are emergency, or breakdown, maintenance and preventive maintenance. Emergency maintenance activities include repairs to production equipment when it exhibits signs of failure or after failure has occurred. Reliance solely on emergency maintenance is characterized as a reactive approach that may adversly a!ect both the integrity of the production plan and the quality of the product.
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Preventive maintenance is a proactive approach that supports the establishment of a JIT environment by studying situations that might interrupt the production plan. Its objective is to increase the reliability of a system over the long term by reducing wear, corrosion, fatigue, and related phenomena [11]. If plant management wants equipment to operate a larger percentage of time, the amount of preventive maintenance applied to that equipment should be increased [12]. As more resources are allocated to preventive maintenance activities, those required for emergency maintenance activities tend to decrease [8]. It should be noted, however, that scheduled maintenance will have a positive impact on reducing equipment failure only when the equipment exhibits an increasing failure rate [11,13]. The model described in this article provides for performance of both interval-based and run-based preventive maintenance activities. The interval-, or calendar-, based maintenance activities are divided into classes based on intervals of time. In this model, we use categories for weekly activities, monthly activities, and quarterly activities. We assume four weeks per month, 12 weeks per quarter, and 48 weeks per year. Run-based maintenance policies, which require preventive maintenance activities based on the cumulative usage of each work center, are set at levels ranging from every 25 h to every 4800 h of work center usage. It is assumed that the performance of any interval-based and run-based activity will return production equipment to `as-newa condition.
3. Phase one: The aggregate planning model Aggregate production planning is performed under managerial constraints that re#ect organization policy in regard to manpower adjustments, the holding of inventory, and outsourcing to other organizations. The APP attempts to minimize costs given a set of aggregate production and preventive maintenance requirements. The aggregate production planning model described in this article uses a mixed-integer linear programming (LP) formulation to determine the aggregate policies for the rate of production, inventory, regular and overtime workforce, and workforce smoothing activities. Subcontracting and backlogging are not considered at the aggregate level in this study. The model deals with the aggregate planning problem at the product family level. We de"ne a product family as a grouping of end items that share a common manufacturing setup. The model assumes that no scrap allowances and that no idle work in process inventories exist. This implies that the operations are at maximum e$ciency, where nothing is wasted or left idle. It assumes that all raw materials and components are available as required and that the workforce is completely interchangeable for di!erent operations at di!erent workstations. The aggregate model includes aggregate requirements for proactive maintenance activities speci"ed by the maintenance policy. Reactive maintenance activities are considered in the simulation
The following example is presented to clarify the di!erence between interval-based and run-based preventive maintenance policies: Changing the oil in your car every three months is an example of an interval-based maintenance policy. In contrast, changing the oil every 3000 miles, regardless of the time elapsed since the previous oil change, is an example of a run-based maintenance policy.
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model rather than at the aggregate level. Because we do not plan machine failure, the costs associated with these failures, including emergency maintenance, should not be included in the aggregate model. Because preventive maintenance activities are performed by machine operators in this model, the production and maintenance requirements share common labor and time resources at the aggregate level. LINGO software [14] is used to solve the aggregate model, with the program output exported to a "le for use in the second phase of the model, master production scheduling. The aggregate planning model is as follows: , 2 2 Min [s d(X )#v X #h I ]# [c H #c F #c O #c = ] GR GR GR GR GR GR FR R DR R MR R PR R G R R 2 ) # M d (M ) IR IR R I subject to , , 2 ) = #O ! a X ! b d(X )! k d (M )*0, I IR R R G GR G GR GR GR R I I !I #X "D , G R\ GR GR GR = != !H #F "0, R R\ R R O !h= )0, R R !Q d(X )#X )0, G GR GR d(X )"1 if X '0, GR GR if X "0, d(X )"0 GR GR X , I , H , F , O , = *0, GR GR R R R R where X production level (in units) of product family i in aggregate period t, GR I inventory level (in units) of product family i in aggregate period t, GR D demand (in units) for product family i in aggregate period t, GR H hiring (in labor hours) in aggregate period t, R F "ring (in labor hours) in aggregate period t, R O overtime (in labor hours) in aggregate period t, R = regular time workforce level (in labor hours) in aggregate period t, R v unit (variable) production cost of product family i in aggregate period t, GR h unit inventory carrying cost of product family i in aggregate period t, GR c hiring cost per labor hour, FR c "ring cost per labor hour, DR c overtime cost per labor hour, MR c regular time workforce cost per labor hour, PR
(1) (2) (3) (4) (5) (6)
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a average labor hours consumed by per unit output of product family i, G h fraction de"ning maximum allowed overtime in any period, N total number of product families, ¹ length of the planning horizon, k work center where maintenance activity is to be performed, s setup cost of product family i, GR d(X ) binary setup variable for product i in aggregate period t, GR b setup time in labor hours for product family i, G M cost per maintenance activity for work center k in period t, IR d (M ) maintenance variable for work center k in week t, IR k maintenance time in labor hours for work center k, I Q a large number used to ensure the e!ects of binary variables. G The "rst constraint ensures that the regular and overtime labor capacity for each aggregate period is su$cient for production, setup, and preventive maintenance activities. The maintenance binary variable for preventive maintenance activities is driven by the maintenance policy determined by the decision maker. For example, an interval-based seasonal maintenance policy implies that resources must be allocated for a single maintenance activity every three periods. Run-based policies, on the other hand, are translated into aggregate requirements based upon work center run times generated in the simulation using the product resource pro"les (Fig. 1) and the FAS. The speci"c length of time for each maintenance activity, k , is set by the requirements for the particular I work center. Constraint two is the basic inventory identity relationship for each product family. Constraint three expresses the workforce balance relationship from period to period. Constraint four states that the overtime used should not exceed a speci"ed percentage of the regular time workforce level in each period. Constraint "ve works as a surrogate constraint for the binary variables in constraint six. Constraint six forces d(X ) to zero when X '0. Q is de"ned as the GR GR G maximum production quantity for a product family during each aggregate period.
4. Phase two: The master schedule Master production scheduling is concerned with what is known as the lot sizing problem. In our model, the MPS is formulated using a multiple goal linear programming model. The MPS is solved using LINGO software [14] with data imported from the aggregate model. 2 , Min bIBI # (w\d\#w>d>) G GRY R R R G IZ)G RYZLR , 2 # (w\d\#w>d>#w\d\#w>d>) G GR G GR G GR G GR G R
In order to create an initial APP using run-based preventive maintenance activities, a "nal assembly schedule "rst must be generated based upon an APP without maintenance resource allocations. This procedure is described on Section 5.
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subject to II !II #XI #BI !BI "DI , RY\ GRY GRY GRY RY\ GRY G ( , (rI X )#d\!d> GKH G RY>G\K RY RY G IZIG K H , 2 ) "0.25 = ! b d(X )! k d (M ) , I IR R G GR G R I d>#d\!d>"0 , RY R R R RYZLR
(1 )
XI #d\!d>"X , GRY GR GR GR IZIG RYZLR
(4 )
(2 ) (3 )
(5 ) II #d\!d>"I , GRY GR GR GR IZIG RYZLR XI , II , BI , d\, d>, d\, d>, d\, d>, d\, d>*0, GRY GRY GRY GRY GRY GRY GRY GRY GRY R R where bI backorder cost per unit for end item k in family i, G wL weights assigned to deviation variables, G XI production quantity (in units) of end product k of product family i in period t , GRY II inventory (in units) of end item k of product family i in period t , GRY BI backorder (in units) of end item k of product family i in period t , GRY DI demand (in units) of end item k of product family i in period t , GRY d\ undertime in period t ; i.e., negative deviation from planned workforce level, RY d> overtime in period t ; i.e., positive deviation from planned workforce level, RY d\ negative deviation from planned aggregate production level of product family i in period t, GR d> positive deviation from planned aggregate production level of product family i in period t, GR d\ negative deviation from planned aggregate inventory level of product family i in period t, GR d> positive deviation from planned aggregate inventory level of product family i in period t, GR d\ negative deviation from planned overtime level, R d> positive deviation from planned overtime level, R rI number of labor hours required for processing item k of product family i at work center GKH j in the mth period since production started on k, assuming at most one operation for each item at each work center j. The objective function in this model attempts to minimize the sum of backordering costs and weighted deviations from goals for production, inventory, and overtime as established by the aggregate production planning model. The aggregate decisions from the previous phase appear as right-hand side values for a series of multiple goal constraints in the linear programming model. The model allows the user to set weights to re#ect the relative importance of each goal established in the aggregate production planning process. For this experiment all weights are set equal to one.
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Fig. 1. Product Resource Pro"les.
The "rst constraint is the inventory identity relationship with backorders incorporated for each item of a particular product family. The second constraint ensures that the total labor hours required at all work centers with undertime and overtime adjustments will not exceed the labor hour capacity planned, or available for, each disaggregate period. Information on the right-hand side obtained from the APP indicates the total labor hours planned for the aggregate period minus labor hours consumed for setups of all product families and for performance of preventive maintenance activities. The `0.25a converts the monthly aggregate "gures into weekly disaggregate
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quantities. The third constraint states that the use of overtime should be targeted at the overtime speci"ed in the aggregate plan. The fourth constraint states that the sum of all end item production quantities for the disaggregate periods (t ) shall be targeted at the aggregate family production levels established for the aggregate periods (t). The last constraint relates the sum of all item inventory quantities in each disaggregate period t to the inventory goal for each aggregate family established for that period t.
5. Phase three: Simulation of the master production schedule and maintenance plan In the third phase of the model, a discrete event simulation is used to evaluate the consequences of the work center loading required to satisfy the MPS established in the previous phase. The MPS, determined by the goal programming model, is exported into the simulation database. That database also contains the following information: the resource pro"les for all end items (Fig. 1), the values of the shape and scale parameters for the failure distribution of each work center, the values of the parameters for the distribution of the repair times for each work center, the hourly costs assigned to equipment emergency service time, and the activity times at which preventive maintenance activities occur. (Preventive maintenance costs are determined at the aggregate level and are not accrued in the simulation.) The model generates a report based on the results of 48 weeks of simulation activities. The report includes speci"c times of work center failure as determined by the simulation program; the lengths of the individual and total emergency repair times, also determined by the simulation program and based on service time distribution parameters; total work center run time; and failure cost for the speci"c maintenance policy, calculated using the treatment's hourly cost for emergency repair and the expected total repair time. The failure cost is added to the aggregate costs determined in the APP model to derive a total policy cost. The simulation program allows the user to evaluate the consequences of the maintenance policy on completion of the MPS. In order to evaluate an interval-based maintenance policy, the decision maker begins with the aggregate model and assigns to the appropriate aggregate periods the resource requirements for that policy. Next, the APP and an MPS are calculated. The simulation program evaluates the MPS and determines speci"c equipment failure times at each work center, the corresponding repair times for emergency maintenance, and total cost for the maintenance policy. In the case of a run-based maintenance policy, the entire model "rst must be run without maintenance resource requirements in order to determine the cumulative run times (CRTs) at each work center. These CRTs are used to assign resource requirements for run-based preventive maintenance activities in the aggregate model. The model then is rerun to generate the new CRTs and to determine the revised maintenance assignments. The process is repeated until the assignments for the run-based preventive maintenance activities for two consecutive runs are identical. The simulation results for the last set of maintenance assignments are used to evaluate that policy. Because the work center mean-time-to-failure values and the repair times generated by the simulation both are based on probability distributions, a degree of uncertainty obviously will be associated with the outcomes from the model. Therefore, each simulation has been replicated 50
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times, and the average value for the simulation results of each treatment has been used for the evaluation of the maintenance policy.
6. Experimental parameters In testing the four sets of hypotheses relating to integration of maintenance and production planning, 252 di!erent experimental treatments were used to model various combinations of policies for (1) maintenance policy, (2) the cost for performing each maintenance activity, (3) the cost used to re#ect the signi"cance of equipment failure, (4) a scale parameter to re#ect equipment failure, and (5) the aggregate strategy. For example, a treatment could call for a maintenance policy of quarterly activities, a maintenance activity cost of $20 per hour, a failure cost of $10 per hour, a scale parameter of 400 h, and a level aggregate strategy. The treatments are summarized in [9]. Experimental treatments for interval-based maintenance policies specify weekly activities, monthly activities, and quarterly activities. Experimental treatments for run-based maintenance policies specify 25, 100, or 400% of the equipment failure distribution scale parameter (in hours) of the Weibull distribution used to model the failure distribution of the work center. For example, when the scale parameter was set at 100 h, run-based policies for experimental treatments speci"ed preventive maintenance activities every 25, 100, or 400 h. The individual activity costs and times for preventive maintenance activities were set at three levels: $20 and one hour per activity, $40 and two hours per activity, and $100 and "ve hours per activity. This article will not investigate the issue of "nancial consequences of equipment failure to the organization. However, several possible consequences could result when equipment fails. For example, severely damaged equipment may require signi"cant expenditures for repair or replacement of parts. Equipment failure may also result in lost production time, with overtime cost penalties incurred when labor resources are used to perform corrective repairs rather than to satisfy production requirements. Unsatisfactory product quality may also result from equipment failure. Equipment experiencing failure may continue to produce parts that do not meet quality standards. These products will have to be inspected, evaluated, and then reworked or scrapped. A high failure cost environment suggests that stability for the production plan is important and that considerable "nancial consequences may result if that plan is interrupted. It may also indicate a premium cost penalty for emergency maintenance activities. A low failure cost environment implies that stability of the production plan is not critical and that the costs incurred from that instability are minimal. In our model, "nancial consequences are modeled by the cost per hour for unscheduled service time. Service times are randomly generated by the simulation model and follow a negative exponential distribution with a mean of "ve hours. The costs for unscheduled service times are set at $10, $50, and $100 per hour. For this experiment, these costs are assumed to be linear with respect to time. Lewis [11] suggests using the two-parameter Weibull distribution to model the distribution of equipment mean-time-to-failure. The shape parameter for the Weibull distribution was "xed at 2.0 for all treatments. This parameter determines the basic shape of the graph of the probability density function. The use of a positive value for the shape parameter indicates the equipment exhibits an increasing rate of failure and thus, would bene"t from the performance of preventive maintenance activities. The scale parameter represents the characteristic life of the distribution and was set at 100, 400, or 1200 h.
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Fig. 2. Summary of Cost Data for the Aggregate Production Planning Model.
The experiment simulated production at two work centers that process items speci"ed in the MPS. Machine loading was determined by rough cut capacity planning through resource pro"les technique using the production requirements speci"ed in Fig. 1. In this "gure, the product resource pro"les for four end items are illustrated. Each line indicates the work center in which the activity is performed, the week in which the activity is performed, and the length of time the activity requires. The production costs included in the APP model include the machine setups; the variable, or material cost for each product produced; costs for holding inventory; costs for hiring and "ring; costs for overtime; and costs for production labor. The production costs are summarized in Fig. 2.
7. The hypotheses Each of the research hypotheses used to test the four sets of hypotheses is repeated below, along with a brief description of the statistical test used. The test result is then summarized and conclusions stated. Hypothesis 1. Integrating maintenance policy with aggregate production planning will signi"cantly in#uence total cost reduction. Statistical analysis was performed at the Wright State University Statistical Consulting Center by Dr. Kathleen Beal.
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Research [15] has shown that managerial policies for aggregate production planning will have a signi"cant in#uence on the cost of the APP. The "rst hypothesis tests whether managerial policies for maintenance planning will have a similar in#uence by testing the e!ectiveness of using the model to reduce total costs for production, preventive maintenance, and emergency maintenance activities. The evaluation criterion for this hypothesis is percent reduction in total costs of a policy using preventive maintenance activities when compared to one relying solely on emergency maintenance activities. A two-tailed, one-sample t test is used to test this hypothesis at the 0.05 level of signi"cance. The calculated test statistic, t"2.6378, and the null hypothesis is rejected (0.01(p(0.02). The alternative, or research, hypothesis is accepted with the conclusion that integrating maintenance policy with aggregate production planning using our model will have a signi"cant in#uence on total cost reduction. Hypothesis 2a. The e!ectiveness of integrating maintenance planning with production planning will escalate with increasing "nancial consequences for equipment failure. Research has shown that the maintenance policy will a!ect the frequency of equipment failure [8]. Therefore, it is logical that the "nancial consequences of equipment failure will be an important factor in the e!ectiveness of this model in reducing costs. As costs associated with equipment failure increase, we would intuitively expect model e!ectiveness likewise to increase. The second hypothesis was tested using the Jonckheere distribution-free test for ordered alternatives. The null hypothesis states that the average e!ectiveness will not be a!ected by increasing "nancial consequence for equipment failure. This indicates that model e!ectiveness and "nancial consequences for equipment failure are independent. The alternative hypothesis states that the average e!ectiveness will increase with increasing "nancial consequences for equipment failure, indicating a relationship between model e!ectiveness and equipment failure. The resulting z score using the large sample approximation formulation is 7.968. Therefore the null hypothesis is rejected at a(0.00003. This clearly indicates that the e!ectiveness of integrating maintenance and production planning increases with escalating "nancial consequences for equipment failure. We can expect that our model will be more e!ective in an environment in which interruptions to the production plan are more signi"cant. Hypothesis 2b. The e!ectiveness of integrating maintenance planning with production planning is signi"cantly reduced by increases in costs for performance of preventive and emergency maintenance activities. This hypothesis tests whether the model e!ectiveness is in#uenced by increasing costs for performance of preventive and emergency maintenance activities. The Jonckheere distribution-free test for ordered alternatives is used to test this research hypothesis at two levels of maintenance costs. The test statistics are Z"4.032 (p(0.00003) and Z"3.438 (p"0.00029). The null hypothesis is rejected, indicating that the e!ectiveness of integrating maintenance planning with production planning signi"cantly decreases as costs for performing preventive and emergency maintenance activities increase relative to costs for production activities. This implies that as maintenance
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costs rise in relation to production costs and costs associated with equipment failure, the potential savings from integrating production and maintenance planning are reduced. Hypothesis 3a. The frequency of preventive maintenance activities required for minimizing total costs is in#uenced by the "nancial consequences of equipment failure. This research hypothesis proposes that there is a relationship between (1) frequency of preventive maintenance activities required by a particular maintenance policy necessary to minimize total costs and (2) "nancial consequences for equipment failure. This is to say that frequency of preventive maintenance activities in an optimum maintenance policy and failure signi"cance are dependent. As the "nancial consequences for equipment failure increase, one would expect total costs to be reduced when policies are adopted requiring increased frequency of preventive maintenance activities. The Chi-square test for independence was used to test this hypothesis. The test statistic of 31.0 indicates that the null hypothesis can be rejected at the a(0.005 level of signi"cance: There is a signi"cant interaction between the signi"cance of equipment failure and the frequency of preventive maintenance required to minimize total costs. Hypothesis 3b. The frequency of preventive maintenance activities required for minimizing total costs is in#uenced by the cost of performing preventive maintenance activities. This hypothesis examines whether there is a relationship (dependence) between frequency of preventive maintenance activities required in an optimal maintenance policy and the hourly cost of performing preventive maintenance activities. As the costs for performing individual preventive maintenance activities increases, one could intuitively expect that total costs for maintenance and production activities would be minimized by policies requiring performance of fewer preventive maintenance activities. The Chi-square test for proportions was used to test this research hypothesis at three levels of failure costs. The null hypothesis was rejected at the 0.005 level of signi"cance for two lower failure costs, but was only rejected at the 0.01 level of signi"cance for the highest level of failure costs. Chi-square values for the three test statistics moved from 31 to 22 to 14 as failure costs increased. This demonstrates that the frequency of preventive maintenance activities required in an optimum maintenance policy is signi"cantly in#uenced by the hourly cost of performing preventive maintenance activities. However, this in#uence appears to diminish as the signi"cance of equipment failure increases. Therefore, in selecting an optimal maintenance policy, the decision maker must consider the in#uences of both the hourly cost for performing preventive maintenance activities and the level of "nancial signi"cance for equipment failure. If either were to vary, the decision maker would need to reconsider the organization's maintenance policy. Hypothesis 4a. In a production environment employing an aggregate strategy of level production, there will be a signi"cant di!erence in e!ectiveness for overall cost reduction between a policy of run-based preventive maintenance and interval-based preventive maintenance activities.
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Hypothesis 4b. In a production environment employing a chase aggregate strategy of varying production with demand, there will be a signi"cant di!erence in e!ectiveness for overall cost reduction between a policy of run-based preventive maintenance and interval-based preventive maintenance activities. These hypotheses were used to test whether the aggregate strategy used in production planning has a signi"cant in#uence on the choice between a run-based or interval-based maintenance policy. A level aggregate production strategy prescribes a constant production rate. Once an appropriate interval for maintenance activities that would minimize total costs is selected, that policy remains optimum unless end item demand varies between aggregate periods. A chase aggregate production strategy, on the other hand, dictates that we vary production with changes in demand. If demand is constant, then production will be constant. If demand exhibits characteristics of seasonality or cycles, or if it simply varies randomly or according to some probability distribution, the volume of production activities would vary during the aggregate period. The activities called for by the maintenance policy might be optimum during one period, but inadequate to maintain the equipment during another. The Chi-square test for independence was used to test hypotheses 4a and 4b. For hypothesis 4a, the test statistic s"0.07407. The null hypothesis cannot be rejected at the a"0.05 level of signi"cance (0.75'p'0.90). This implies that in a production environment employing a level aggregate strategy, there will not be a signi"cant di!erence in overall cost reduction between using a policy of run-based preventive maintenance or of interval-based preventive maintenance activities. For hypothesis 4b, the test statistic s"16.16. The null hypothesis is rejected at the a"0.05 level of signi"cance (p(0.005). In a production environment employing a chase aggregate strategy, we can expect that run-based maintenance policies will be more e!ective than interval-based policies during a signi"cant portion of the time. The experiment results demonstrate that when there is a level aggregate strategy, there will not be a signi"cant di!erence in total cost when we select either a run-based or an interval-based policy. The hours of production at each work center will be constant during the aggregate planning period. In practice, therefore, an interval-based maintenance policy may be as equally e!ective as a runbased policy. In an environment employing a chase aggregate strategy, on the other hand, run-based maintenance policies generally will be more e!ective than interval-based policies and should therefore be selected by the decision maker.
8. Managerial implications In this study, we introduced a model that links selection of the organization's maintenance policy with the aggregate production planning process. We developed an experimental design and used it to evaluate a set of four hypotheses in order to test our model. The managerial implications of the test results are summarized below and may be used to guide decision makers in the application of this model. It should be noted, however, that the test results are subject to the assumptions of our experiment and cannot blindly be applied beyond the limitations of the experiment.
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E Under certain conditions, integrating maintenance and production planning is an e!ective approach to reducing total costs for production activities, preventive maintenance activities, and the costs associated with equipment failure. An integrated approach allows the decision maker to more accurately determine the point at which the sum of these is minimized. E The e!ectiveness of integrating maintenance planning with production planning in reducing total costs will increase as "nancial consequences for equipment failure increases. E The expense of performing preventive maintenance may be a signi"cant factor in determining the optimum maintenance policy. As the costs to perform preventive maintenance activities increase, the potential bene"t of integrating production and maintenance planning appears to decrease. That bene"t, however, is tied to the "nancial signi"cance of equipment failure. Neither factor should be considered without regard for the other. E As the "nancial signi"cance of equipment failure increases, organizations will minimize total costs by adopting maintenance policies requiring more frequent maintenance activities. E The frequency of maintenance activities required for an optimum maintenance policy is a!ected by the cost to perform preventive maintenance activities. As failure costs increase, and other factors remain unchanged, policies calling for more frequent maintenance activities will be optimal. This trend is blocked, however, when the production activity costs also increase. E The selection of an optimum maintenance policy is in#uenced by both aggregate production policy and end item demand pattern. An organization using a chase aggregate production strategy with a varying demand pattern should select a preventive maintenance policy based on equipment run time. An organization with a constant demand pattern will not signi"cantly bene"t from using one type of preventive maintenance policy over the other. E An organization using a level aggregate production strategy, under either a constant or varying demand pattern, also will not signi"cantly bene"t from using one type of maintenance policy over the other. Additional research from this study may follow several directions. One path might be to make an empirical study of manufacturing organizations, comparing the e!ectiveness of their current maintenance policies with the theoretical policy resulting from this model. Another direction might be to evaluate the impact of the model on schedule e!ectiveness measures such as throughout and makespan. A third direction would be to evaluate the in#uences of additional equipment failure and service distributions on the model's e!ectiveness. Each of these would be a natural extension of the research already conducted.
References [1] Chung CH, Krajewski LJ. Planning horizons for master production scheduling. Operations Management 1984;4:389}406. [2] Gilbert JP, Finch BJ. Maintenance management: keeping up with production's changing trends and technology. Journal of Operations Management 1985;6:1}12. [3] Vollmann TE, Berry WL, Whybark D. Manufacturing planning and control systems. Boston: Irwin, 1997. [4] Krajewski LJ, Ritzman LP. Disaggregation in manufacturing and service organizations. Decision Sciences 1977;8:1}18.
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[5] Chung CH. Planning horizons for aggregate planning and master production scheduling. Dissertation, Ohio State University, 1982. [6] Nakajima S. Introduction to TPM. Cambridge: Productivity Press, 1988. [7] Rhyne DM. Total plant performance advantages through total production maintenance. APICS Conference Proceedings, rpt. APICS Curricula and Certi"cation Council, 1991. [8] Rishel TD. A model of the e!ect of scheduled maintenance on manufacturing system capacity. Dissertation, The Pennsylvania State University, 1991. [9] Weinstein L. Decision support for the integration of maintenance activities with fron end production planning activities. Dissertation, The University of Kentucky, 1996. [10] Ettkin LP, Jahnig DG. Adapting MRP II for maintenance resource management can provide a strategic advantage. Industrial Engineering 1986;50}9. [11] Lewis EE. Introduction to reliability engineering. New York: Wiley, 1987. [12] Mann L. Maintenance management. Lexington, MA: D.C. Heath and Company, 1976. [13] Rishel TD, Cristy DP. Incorporating maintenance activities into production planning: integration at the master schedule versus material requirements level. unpublished manuscript. [14] LINGO. Lindo Systems Inc. Chicago, IL, 1992. [15] Mangiameli PM. The e!ects of managerial policies on aggregate plans, the master production schedule, and departmental plans. Dissertation, Ohio State University, 1979.
Larry Weinstein is an Assistant Professor of Operations Management at Wright State University in Dayton, OH 45435. He received his doctorate from the University of Kentucky in 1996. He has taught at Eastern Kentucky University and Ball State University. Dr. Weinstein teaches courses in Statistics, Operations Management, and Quality Management. Chen H. Chung graduated from Ohio State University with a Ph.D. in Production and Operations Management. He is currently Professor of Decision Science and Information Systems and Gatton Research Professor at School of Management, Gatton College of Business and Economics of University of Kentucky. He is Certi"ed Fellow in Production and Inventory Management (CFPIM) by APICS. Dr. Chung has published over forty articles in journals such as Journal of Operations Management, Decision Sciences, International Journal of Production Research, Production and Operations Management, European Journal of Operational Research, Computers & Operations Research, and the Journal of Manufacturing Management.